Carlos harvests cassavas at a constant rate. He needs $35$ minutes to harvest a total of $15$ cassavas. Write an equation to describe the relationship between $t$, the time, and $c$, the total number of cassavas.
Answer: Let's find the constant of proportionality. In the proportional relationship between $t$, the time, and $c$, the total number of cassavas, one constant of proportionality is the number of cassavas harvested per minute. It is the number we multiply by the time to get the total number of cassavas. $t\,\times\, ?=c$ $\begin{aligned} t\,\times\, {?}&=c \\\\ {?}&=\dfrac{c}{t} \\\\ &=\dfrac{15}{35} \\\\ &=\dfrac{3\times\cancel{5}}{7\times\cancel{5}} \\\\ &={\dfrac{3}{7}} \end{aligned}$ The constant of proportionality is ${\dfrac{3}{7}}$. This means we can multiply ${\dfrac{3}{7}}$ by the time to get the total number of cassavas. Now, let's write the equation: $\begin{aligned} \text{total number of cassavas}&={\text{cassavas per minute}}\times\text{minutes} \\\\ c&={\dfrac{3}{7}}t \end{aligned}$ One correct equation is: $c=\dfrac{3}{7}t$